Adultery can be a reason for granting divorce.
Further, under Hindu Marriage Act 1955, (assuming you are a Hindu) adultery is one of the grounds for seeking divorce.
Section 13 of the Hindu Marriage Act provides the various grounds on which divorce can besought by one of the parties to a marriage. It is as follows:
Section 13(1) states that a petition may be presented by either the husband or the wife, for dissolution of marriage by a decree of divorce on the ground that the otherparty-
i. has, after the solemnization of the marriage, had voluntary, sexual intercourse with any person other than his or her spouse; or
a. has, after the solemnization of the marriage, treated the petitioner with cruelty; or
In view of aforesaid , you can file a divorce petition under Section 13 (1) (i) and Section 13 (1) (ia) on the grounds of adultery and cruelty, and seek dissolution of marriage. It is pertinent to mention here, that to prove adultery is generally very difficult, wherein the onus of proof is usually on the petitioner and you need to have strong and cogent evidence to prove that she has committed adultery. The evidence stated in your query will have to be examined to conclude whether they are strong and cogent evidence to prove adultery.
Further, with respect to custody of your child, your child is minor and you need to file a petition for the custody of the child. Section 6 of The Hindu Minority and Guardianship Act states that the ‘natural guardian of a Hindu minor, in respect of the minor’s person as well as in respect of the minor’s property …. in the case of a boy or unmarried girl is the father, and after him, the mother, provided that the custody of a minor who has not completed the age of five years shall ordinarily be with the mother.